Let’s examine Magee’s fall using elementary physics. Homework Problem 29 in Chapter 2 of Intermediate Physics for Medicine and Biology explains how someone falling through the air reaches a steady-state, or terminal, speed. A typical terminal speed, v, when skydiving is about 50 m/s. This may be a little slower than average, but v decreases with mass and ball turret gunners like Magee were usually small. Skydivers will reach their terminal speed after about 20 seconds. Magee fell for much longer than that, so starting four miles up didn’t matter. He could have begun forty miles up and his terminal speed would have been the same (presumably he would have suffocated, but that’s another story).
When falling, what kills you is the sudden deceleration when you hit the ground. Suppose you’re traveling at v = 50 m/s and you hit a hard surface like cement. You come to a stop over a distance, h, of a few centimeters (a person isn’t rigid, so there would be some distance that corresponds to the body splatting). Let’s estimate 10 cm, or h = 0.1 m. If the acceleration, a, is uniform, we can use an equation from kinematics to calculate a from v and h: a = v^2/(2 h) = 50^2/0.2 = 12,500 m/s^2. This is about 1250 g, where g is the acceleration of gravity (approximately 10 m/s^2).
How much acceleration can a person survive? It’s hard to say. Some roller coasters can accelerate at up to 3 g and you feel a thrill. Astronauts in the Mercury space program experienced about 10 g during reentry and they survived. Flight surgeon John Stapp withstood 46 g on a rocket sled, but that is probably near the maximum. Clearly 1250 g is well over the threshold of survivability. You would die.
So, how did Magee survive? He didn’t hit cement. Instead, he crashed through the glass ceiling of the St. Nazaire railroad station. Most sources I’ve read claim that shattering the glass helped break his fall. Maybe, but I have another idea. Some of the articles I’ve examined have German soldiers finding Magee alive on the station floor, but others say he was found tangled in steel girders. Below is a picture of the railroad station as it looked during World War II.
Notice the structures below the glass ceiling. I wouldn’t call them girders or struts. To me they look like a web of steel cables or ties. My hypothesis is that this web functioned as a net. Suppose Magee landed on one of the ties and it deflected downward, perhaps dragging part of the ceiling with it, or pulling down other ties, or breaking at one end, or stretching like a bungee cord. All this pulling and breaking and stretching would reduce his deceleration. Let’s guess that he came to rest about three meters below where he first hit a tie. Now his acceleration (assuming it’s uniform) is a = 50^2/6 = 417 m/s^2, or about 42 g. That’s a big deceleration, but it may be survivable. You would expect him to be hurt, and he was; he suffered from several broken bones, damage to a lung and kidney, and a nearly severed arm.
If my hypothesis is correct, the shattering of glass had little or nothing to do with breaking Magee’s fall. I’m sure it made a loud noise, and must have given the accident a dramatic flair, but the glass ceiling may have been irrelevant to his survival.
I don’t think we can ever know for sure why Magee didn’t die, short of building a replica of the train station, dropping corpses (or, more hygienically, crash dummies) through the roof, and video recording their fall. Still, it’s fun to speculate.
After the crash, what happened to Magee? He was captured, became a prisoner of war, and was treated for his injuries. In May 1945 the war in Europe ended and he was freed. He returned to the United States and lived another 58 years. He was awarded the Air Medal and a well-earned Purple Heart. Alan Magee’s survival represents a fascinating example of physics applied to medicine and biology.
Originally published at http://hobbieroth.blogspot.com.